Hi Colin,
I have this issue with Microsoft Excel for Mac 2011 as well, only when using data in ArcGIS Pro.
IN ARCMAP
I can take an Excel for Mac file into ArcMap and it recognizes the first row as field values:

I can then successfully Display XY data in ArcMap:

And I can successfully save this XY layer as a shape file:

I can successfully use the Microsoft Excel for Mac 2011 data in ArcMap without problems.
IN ARCGIS PRO
When I open this SAME file in ArcGIS Pro, the program does not recognize the first row as field values:

I am unable to display XY data with this table:

I am also unable to export this table, receiving an error message that the file cannot be exported to any location with spaces in the file path. Note, the default file path has spaces in it.
MY CURRENT WORKAROUND
Right now in order to work around the problem I have to load the data first into ArcMap to generate a Shapefile that can be read by ArcGIS Pro/BAO.
RELATED TO EXISTING BUG REPORT?
I have similar issues using this data with BAO, and I believe that there is a bug report on it that was submitted in 2012. From what I understand the architecture of BAO and ArcGIS Pro are similar. Please investigate if this is part of the existing bug report with Mac/Excel, or requires a new bug report.
